关于非光滑域上具有接触项的泛函的松弛

IF 1.2 2区数学 Q1 MATHEMATICS

Indiana University Mathematics Journal Pub Date : 2020-10-07 DOI:10.1512/iumj.2023.72.9211

R. Cristoferi, G. Gravina

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引用次数: 0

摘要

给出了$BV(0)中的松弛的积分表示公式;\R^M)$关于L^1(o;具有边界接触能项的泛函。这一特性适用于大范围的表面能密度，以及满足温和规则性假设的域。通过一些经典的下半连续性失效的例子，我们分析了集合几何进入松弛过程的程度。

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On the relaxation of functionals with contact terms on non-smooth domains

We provide the integral representation formula for the relaxation in $BV(o; \R^M)$ with respect to strong convergence in $L^1(o; \R^M)$ of a functional with a boundary contact energy term. This characterization is valid for a large class of surface energy densities, and for domains satisfying mild regularity assumptions. Motivated by some classical examples where lower semicontinuity fails, we analyze the extent to which the geometry of the set enters the relaxation procedure.

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